How to Divide a Square into Thirds 

Evan, it is close enough not just for most origami purposes, but for all origami purposes. The final crease angle at the corner is 33.75 degrees. This can easily be calculated by the bisections. Using trigonometry the tangent of 33.75 will tell us exactly how far down a square side of length one the crease lands. To 3 decimal places this is .668 and to three decimal places the actual 2/3 mark is .667. So the folding method is off by about one thousandth the length of square's side. For all practical folding purposes regardless of the folding accuracy desired, it makes no difference.

you are so good at explaining

Brilliant! Really enjoyed watching the magic happen! Thank you for the learning

but what if i don't want dotted lines to keep appearing in my folds???

2 years later... You have no idea how much I have been struggling to create a paper pattern for a tree skirt using math to figure out the shapes within the skirt that will determine where the various color fabrics will be, (and how much of each fabric to buy!). The 3rds thing was killing me! THIS IS SO MUCH EASIER!!! Very glad you posted. Thank you.

Thank you soooo much? This helped me in hundred of thousands of my origami models.👌👌👌👍👍👍

Actually, this is not correct, though a very good approximation. This relies on the supposition that a line 37.5 degrees apart from the side of the square would intersect the other side at 2/3 of its length. In other words, that tan(37.5)=2/3. This equality is false, as tan(37.5)= approx. 0.6682. There is, however, a correct construction, which also requires just 4 or so steps. You just need to intersect the diagonal with the line connecting a vertex with the middle of an opposite side. Correctness of this method follows immediately from Thales' theorem.

How about we measure one side and divide by 3??

This is an approximation, granted, pretty good one for all practical uses but not mathematically solid. It is based on tan((45+22.5)/2) = tan(33.75) ~ 0.668, not perfect 2/3 = 0.666... Correct angle for 2/3 is atan(2/3) = 33.69007... and it can not be build like this. Instead should be based on triangle median theorem where medians are intersecting exactly at 1/3 length. This would require a couple more creases to make a triangle and its medians intersection point.

Thank you very much for the tutorial on how to fold a square into thirds, that was really helpful

Doesn’t work. Has big gap when I try. The tool doesn’t work. How can I fix this?

i really need to divide these 10" X8" X 1/8" planks of purple heart into 3 equal parts across the 10" span, they are to become dividers in a desk topper kind of display thingy, this just saved me tons headache, and ruining some really nice , not to mention expensive wood

Perfect... not too fast, not too slow... clear instructions!!

I’d love to see a proof for the math of why this works! You might not need to know what that is to do this though 😅 but it would be interesting!

Can you teach the math theory behind this?

I'm tryina spilt my edible in 3 parts and this helped

Use a ruler instead 😂😂

Very nice! Thanks so much for this tutorial!

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How do I divide a flap in thirds)

Thank you for this tutorial. It is a big help to me.

Thank you, very clear instructions!

Thank you so much

There's a much easier way to do this, but I really appreciate your clear and precise instructions.

OMG this is AMZING thank you so much

Very nice.

Very good

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thx this relly helpt me till now i was using a ruler lol

Its a great tutorial but i always getcthe folds off by i a bit and the thirds never seem to be equal to me

I thought there were too many creases in the beginning. I watched the tutorial to the end and saw the ‘tool’ which is brilliant! Thanks for sharing!!

Have u done an origami dragon tutorial?

too slow

I checked your method mathematically; it doesn’t work.

Very very very bad